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Metamath Proof Explorer

Theorem nvrel

Description: The class of all normed complex vectors spaces is a relation. (Contributed by NM, 14-Nov-2006) (New usage is discouraged.)

		Ref	Expression
	Assertion	nvrel	$⊢ Rel NrmCVec$

Step	Hyp	Ref	Expression
1		nvss	$⊢ NrmCVec \subseteq {CVec}_{OLD} \times V$
2		relxp	$⊢ Rel ({CVec}_{OLD} \times V)$
3		relss	$⊢ NrmCVec \subseteq {CVec}_{OLD} \times V \to (Rel ({CVec}_{OLD} \times V) \to Rel NrmCVec)$
4	1 2 3	mp2	$⊢ Rel NrmCVec$